Table of Contents
I Standard Mereology
Introduction 3
I The Standard Conception of Composition 9
I.1 Introductory Remarks 9
I.2 Standard Mereology 10
I.2.1 The Basic Concepts of Standard Mereology 11
I.2.2 The Basic Principles of Standard Mereology 15
I.2.3 A Gradual Statement of the Theory 17
I.3 The Application of Standard Mereology to Ordinary Material Objects 20
II Ordinary objects as Mereological Sums 23
II.1 Introductory Remarks 23
II.2 Thomson's Three-Dimensionalist Approach 23
II.3 Lewis' Four-Dimensionalist Approach 29
II.3.1 Support for Unrestricted Composition 29
II.3.1.1 The Lewis/Sider Argument from Vagueness 30
II.3.1.2 The Controversial Premise (P3) 34
II.3.1.3 The Matter of Vague Existence 37
II.3.2 The Composition-as-Identity Thesis 40
II.4 Concluding Remarks 43
III Composition as Non-Identity 45
III.1 Introductory Remarks 45
III.2 The Suspect Strategy 47
III.2.1 The Suspect Strategy and Leibniz's Law 47
III.2.1.1 Contingent Identity 47
III.2.1.2 Temporary Identity 48
III.2.1.3 Indeterminate Identity 51
III.2.2 The Suspect Strategy and Existence Principles: Non-Existent Objects 52
III.2.3 The Suspect Strategy and Restricted Indiscernibility Principles 54
III.2.3.1 Coincident Objects 54
III.2.3.2 Relative Identity 56
III.3 What's Wrong with the Suspect Strategy? 58
III.3.1 The Purely Stipulative Response 58
III.3.2 Gibbard's Appeal to Failures of Substitutivity 61
III.3.3 Parsons' Appeal to the Paradoxes of Naive Set Theory 65
III.3.4 Deutsch's Expansion Principle 66
III.4 Concluding Remarks 67
II A Contemporary Structure-Based Mereology
IV A Different Kind of Whole 71
IV.1 Introductory Remarks 71
IV.2 PartingWays with the Standard Conception 72
IV.2.1 Fine's "Aggregative Objection" 72
IV.2.2 Fine's "Monster Objection" 73
IV.3 Fine's Theory of Embodiments 75
IV.3.1 Rigid Embodiments 76
IV.3.2 Variable Embodiments 78
IV.4 Discussion 82
IV.4.1 The Proliferation of Sui Generis Relations 82
IV.4.2 The Superabundance of Objects 83
IV.4.3 The Mysterious Nature of Variable Embodiments 85
IV.4.4 The Formal Properties of Parthood 88
IV.5 Concluding Remarks 89
III Ancient Structure-Based Mereologies
V The Role of Structure in Plato's Mereological Writings 93
V.1 Introductory Remarks 93
V.2 The Negative Mereological Undercurrent 94
V.3 The Positive Mereological Undercurrent 96
V.4 Platonic Wholes 100
V.4.1 Normativity, Teleology, Intelligibility and Unity 100
V.4.2 Structure and Content 105
V.4.2.1 The Aristotelian Regress in Met. Z.17 108
V.4.2.2 Parts as "Structure-Laden" 112
V.4.2.3 A Final Word on Content 117
V.5 Concluding Remarks 119
VI Aristotle's Refinements of Plato's Theory 122
VI.1 Introductory Remarks 122
VI.2 The Centrality of "Part" and "Whole" in the Aristotelian Corpus 123
VI.3 The Problem of the One and the Many 125
VI.4 A Reading of the Text 126
VI.4.1 One, Divisibility, Part, Quantity and Measure 126
VI.4.2 Kinds of Measure and Principles of Unity 128
VI.4.3 The Ways of Being a Part: Met. .25 134
VI.4.4 The Ways of Being a Whole: Met. .26 139
VI.4.4.1 Wholes and Totals 140
VI.4.4.2 Degrees of Wholeness 142
VI.5 Summary of Sections VI.3-4: The Highlights 150
VI.6 Discussion 157
VI.6.1 The Formal Properties of Parthood 157
VI.6.2 In Search of the Ultimate Mereological Atom 159
VI.7 Concluding Remarks 162
IV An Alternative Structure-Based Theory
VII Objects as Structured Wholes 167
VII.1 Introductory Remarks 167
VII.2 Outlines of the Theory 167
VII.2.1 Mereological Non-Proliferation: A Single Relation of Parthood 167
VII.2.2 The Restricted Nature of Composition 168
VII.2.3 An Ontology of Kinds 170
VII.2.4 Ontology and Mereology 171
VII.2.5 Form and Matter 172
VII.2.6 An Ontology of Structured Wholes 174
VII.2.7 The Dichotomous Nature of Wholes 176
VII.2.7.1 Material Components as Proper Parts 176
VII.2.7.2 Formal Components as Proper Parts 179
VII.2.7.3 Material and Formal Components as Proper Parts 183
VII.2.8 The Hierarchical Nature of Composition 186
VII.2.9 Change over Time 188
VII.2.10 Synchronic and Diachronic Identity 191
VII.2.11 Composition as Non-Identity 192
VII.2.12 The Unified Nature of Wholes 192
VII.3 Concluding Remarks 198
VIII In Defense of Kinds 200
VIII.1 Introductory Remarks 200
VIII.2 What Are Natural Kinds? 201
VIII.3 The Special Features of Natural Kinds 203
VIII.3.1 Induction and Projectibility 204
VIII.3.2 Laws of Nature 205
VIII.3.3 Causation and Explanation 207
VIII.4 Biological Taxa 210
VIII.4.1 The Ontological Status of Species 210
VIII.4.2 Species as Kinds 214
VIII.5 What Sorts of Entities Are Natural Kinds? 219
VIII.5.1 The Semantics of Natural Kind Terms 220
VIII.5.1.1 Rigid Designation 223
VIII.6 Incommensurability and Indeterminacy: Physical and Chemical Kinds 227
VIII.6.1 Impurities and Isotopes: Scientific and Ordinary Classifications 227
VIII.6.2 Meaning-Change and Theory-Change 230
VIII.7 Concluding Remarks 233
IX Structure 235
IX.1 Introductory Remarks 235
IX.2 Some Preliminaries 236
IX.2.1 Related Notions 236
IX.2.2 Different Grammatical Roles 238
IX.2.3 The Gestalt Theorists: Rescher and Oppenheim 239
IX.3 Some Case Studies 240
IX.3.1 Mathematical Structure 240
IX.3.2 Logical Structure 241
IX.3.3 Chemical Structure 244
IX.3.4 Musical Structure 246
IX.3.5 Linguistic Structure 248
IX.4 Structures as Objects 252
IX.5 The Grounding Problem Revisited 254
IX.5.1 A Potential Problem Case 256
IX.5.1.1 The Detachability of the Grounding Problem 256
IX.5.1.2 Giving Up the Transitivity of Parthood 257
IX.5.1.3 Individual Forms and Haecceities 257
IX.5.1.4 Denying the Existence of Heaps 258
IX.6 Concluding Remarks 259
Conclusion 261
Bibliography 265
General Index 281
Index of Names 286
